University of Chicago VIGRE REU 2010

Current and past notes for the REU on Laci Babai's home page [UPDATED] (REU web page)

Notes and reading materials about finite spaces (EXPANDED July 3, 6, 21; Aug. 2) (May Finite)

Two online books for use in the Anno/May algebra course (Books)

Five problem sets on groups and a ``checklist'' for the Anno/May algebra course

  • (pdf1) (pdf2) (pdf3) (pdf4) (pdf5) (Checklist.pdf)

    Four problem sets on complex numbers and Riemann surfaces for the Anno/May algebra course

  • (Complex1.pdf) (Complex2.pdf) (Complex3.pdf) (Complex4.pdf)

    Logic projects from Maryanthe Malliaris (pdf)

    Guides to writing papers (Steve Kleiman and Dan Kleitman, MIT)

  • Writing a math paper (two formats): READ THIS CAREFULLY (pdf) (pdf)
  • Another useful guide: READ THIS TOO (pdf)

    Tex Help

  • Template for texing REU papers: USE THIS TEX FILE (tex) (pdf)
  • An excellent latex web page (with an REU template with more examples) (web page)
  • LaTeX -- A document preparation system (web page)

    • 2010 REU: PARTICIPANT PAPERS -- FULL PROGRAM

  • Carsen Berger. A categorical approach to proofs--as--programs. (pdf)
  • Meru Bhanot. Cutting sequences in Euclidean and hyperbolic geometry. (pdf)
  • John Binder. Unstable first--order theories. (pdf)
  • Samuel Bloom. Basic theory of algebraic geometry. (pdf)
  • William Chan. Limit computable sets and degrees. (pdf)
  • Je--ok Choi. The representations of the symmetric group. (pdf)
  • Andy Dahl. A rigorous introduction to Brownian motion. (pdf)
  • Jasper DeAntonio. The Turing degrees and their lack of linear order. (pdf)
  • Marcello Delgado. Some examples of subdivision of small categories. (pdf)
  • Jonathan Emberton. An introduction to free quantum field theory through Klein--Gordon theory. (pdf)
  • Connie Fan. Reverse mathematics. (pdf)
  • Eugenia Fuchs. Completeness of the random graph: two proofs. (pdf)
  • Jonathan Gleason. Existence and uniqueness of Haar measure. (pdf)
  • Aaron Halper. Ultraproducts and model theory. (pdf)
  • Kris Harper. Group cohomology and Kummer theory. (pdf)
  • Blake Hartley. The heat equation and the Li-Yau Harnack inequality. (pdf)
  • Julian Hartman. First order logic and nonstandard analysis. (pdf)
  • Riley Heckel. Percolation and the existence of the infinite open cluster. (pdf)
  • Daphne Kao. Representations of the symmetric group. (pdf)
  • Dennis Kriventsov. Local wellposedness for the nonlinear Schr\"odinger equation. (pdf)
  • Don Laackman. The Cantor--Schroeder--Bernstein property in categories. (pdf)
  • Jonathan Libgober. The Euler characteristic, Poincar\'e--Hopf theorem, and applications. (pdf)
  • Melissa Lynn. Categories of probability spaces. (pdf)
  • Jonathan Margoliash. Matrix--tree theorem for directed graphs. (pdf)
  • Haney Maxwell. Persistent homology of finite topological spaces. (pdf)
  • Samuel Moy. Applying Gr\"obner bases to ``solve'' solvable polynomials. (pdf)
  • James Murphy. Differential Galois theory. (pdf)
  • Paige North. A foundational category. (pdf)
  • Neel Patel. Irreducible representations of semisimple Lie algebras. (pdf)
  • Vladislav Petkov. Ad\`eles and Id\`eles and their applications. (pdf)
  • David Price. The Gysin sequence and the Hopf invariant. (pdf)
  • David Ramsey. A result on representations of homology manifolds by finite spaces. (pdf)
  • Nick Ramsey. Morley's categoricity theorem. (pdf)
  • James Ready. Markov chains: stationary distributions and functions on state spaces. (pdf)
  • Wolfgang Schmaltz. The Atiyah--Guillemin--Sternberg convexity theorem. (pdf)
  • Jay Shah. Equivariant algebraic topology. (pdf)
  • Alex Stratmann. Fourier series of continuous functions at given points. (pdf)
  • Alex Tolish. General relativity and the Newtonian limit. (pdf)
  • Evan Turner. The Black--Scholes model and extensions. (pdf)
  • Andrew Villadsen. The infinite symmetric product and homology theory. (pdf)
  • Daping Weng. On minimal finite models. (pdf)
  • Isaac Ottani Wilhelm. Some elementary results in representation theory. (pdf)
  • Michael Wong. Interpolation, maximal operators, and the Hilbert transform. (pdf)
  • Alex Zorn. Semisimple Lie algebras and the Chevalley group construction. (pdf)

    2010 REU: PARTICIPANT PAPERS -- APPRENTICE/INTERMEDIATE

  • Timur Akman--Duffy. The class number theorem. (pdf)
  • Aashirwad Anand. A brief study of discrete and fast Fourier transforms. (pdf)
  • James Buchanan. The existence and uniqueness of solutions to differential equations. (pdf)
  • Albert Chang. Isometries of the hyperbolic plane. (pdf)
  • Guo Chen. Marcinkiewicz interpolation. (pdf)
  • Jusvin Dhillon. Hidden Markov models in index returns. (pdf)
  • Raphael Ho. Algebraic topology. (pdf)
  • Amy Hua. An introductory treatment of Morse theory on manifolds. (pdf)
  • Eddie Keefe. The classical risk model with exponentially distributed claims. (pdf)
  • John Kopper. Elliptic curves and cryptography. (pdf)
  • Nina Leung. Uniformly discontinuous groups of isometries of the plane. (pdf)
  • Patrick McQuighan. Simulating the Poisson process. (pdf)
  • Dileep Menon. An introduction to functional analysis. (pdf)
  • Jason Quinones. Finite spaces and Quillen's conjecture. (pdf)
  • Ryan Wang. Markov chain Monte Carlo. (pdf)

    2010 REU: PARTICIPANT PAPERS -- APPRENTICE

  • Ian Alevy. Solutions to the heat and wave equations and the connection to Fourier series. (pdf)
  • Joshua Bosshardt. Sums of squares. (pdf)
  • Xin Cao. Euclidean isometries and surfaces. (pdf)
  • Chaofan Chen. Group theory and the law of quadratic reciprocity. (pdf)
  • Davi da Silva. Metric spaces and differential equations. (pdf)
  • Douglas Everson. Jr. Gauss map. (pdf)
  • John Gallagher. Elementary number theory and the Chinese remainder theorem. (pdf)
  • Grant Rotskoff. The Gauss--Bonnet theorem. (pdf)
  • Abhinav Shrestha. Classification of finite simple groups. (pdf)
  • Watee Srinin. Measure theoretic aspects of dynamical systems. (pdf)
  • Maxwell Stolarski. Frieze groups in $\mathbb{R}^2$. (pdf)
  • Alex Turzillo. Representations of matrix Lie algebras. (pdf)
  • Max Xiong. Topological spaces and the fundamental group. (pdf)
  • Hamming Zhang. Introduction to representation theory and characters. (pdf)